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数学专业英语-Notations and Abbreviations (I) Learn to understand

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发表于 2004-5-6 10:00:41 | 显示全部楼层 |阅读模式
< ><B><FONT face="Times New Roman"><FONT size=3> <p></p></FONT></FONT></B></P>
< ><FONT face="Times New Roman"><FONT size=3>N                    set of natural numbers<p></p></FONT></FONT></P>
< ><FONT face="Times New Roman"><FONT size=3>Z                    set of integers<p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman"><FONT size=3>R                    set of real numbers<p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman"><FONT size=3>C                    set of complex numbers<p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman"><FONT size=3>+                    plus; positive<p></p></FONT></FONT></P>
<P ><FONT size=3>-    <FONT face="Times New Roman">           minus; negative<p></p></FONT></FONT></P>
<P ><FONT size=3>×    <FONT face="Times New Roman">           multiplied by; times<p></p></FONT></FONT></P>
<P ><FONT size=3>÷<FONT face="Times New Roman">                   divided by<p></p></FONT></FONT></P>
<P ><FONT size=3>=<FONT face="Times New Roman">                   equals; is equal to<p></p></FONT></FONT></P>
<P ><FONT size=3>≡<FONT face="Times New Roman">                   identically equal to<p></p></FONT></FONT></P>
<P ><FONT size=3>≈<FONT face="Times New Roman">,</FONT>≌<FONT face="Times New Roman">                 approximately equal to<p></p></FONT></FONT></P>
<P ><FONT size=3>><FONT face="Times New Roman">                   greater than<p></p></FONT></FONT></P>
<P ><FONT size=3>≥<FONT face="Times New Roman">                   greater than or equal to<p></p></FONT></FONT></P>
<P ><FONT size=3><<FONT face="Times New Roman">                   less than<p></p></FONT></FONT></P>
<P ><FONT size=3>≤<FONT face="Times New Roman">                   less than or equal to<p></p></FONT></FONT></P>
<P ><FONT size=3>》<FONT face="Times New Roman">                   much greater than<p></p></FONT></FONT></P>
<P ><FONT size=3>《<FONT face="Times New Roman">                   much less than<p></p></FONT></FONT></P>
<P ><v:shapetype><v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><v:path connecttype="rect" gradientshapeok="t" extrusionok="f"></v:path><lock aspectratio="t" v:ext="edit"></lock></v:shapetype><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                  square root<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                  cube root<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                  nth root<p></p></FONT></FONT></P>
<P ><FONT size=3>│<FONT face="Times New Roman">a</FONT>│<FONT face="Times New Roman">                absolute value of a<p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman"><FONT size=3>n!                    n factorial<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                  a to the power n ; the nth power of a <p></p></FONT></FONT></P>
<P ><FONT size=3><FONT face="Times New Roman">[a]                   the greatest integer</FONT>≤<FONT face="Times New Roman">a<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                the reciprocal of a <p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman"><FONT size=3> <p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman"><FONT size=3>Let A,  B be sets<p></p></FONT></FONT></P>
<P ><FONT size=3>∈    <FONT face="Times New Roman">            belongs to ; be a member of<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                    not belongs to<p></p></FONT></FONT></P>
<P ><FONT size=3><FONT face="Times New Roman">x</FONT>∈<FONT face="Times New Roman">A                  x os amember of A<p></p></FONT></FONT></P>
<P ><FONT size=3>∪<FONT face="Times New Roman">                    union<p></p></FONT></FONT></P>
<P ><FONT size=3><FONT face="Times New Roman">A</FONT>∪<FONT face="Times New Roman">B                 A union B<p></p></FONT></FONT></P>
<P ><FONT size=3>∩<FONT face="Times New Roman">                    intersection<p></p></FONT></FONT></P>
<P ><FONT size=3><FONT face="Times New Roman">A</FONT>∩<FONT face="Times New Roman">B                 A intersection B<p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman" size=3>A</FONT><v:shape><FONT face="Times New Roman"><FONT size=3> <v:imagedata></v:imagedata></FONT></FONT></v:shape><FONT face="Times New Roman"><FONT size=3>B                 A is a subset of B;A is contained in B<p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman" size=3>A</FONT><v:shape><FONT face="Times New Roman"><FONT size=3> <v:imagedata></v:imagedata></FONT></FONT></v:shape><FONT face="Times New Roman"><FONT size=3>B                 A contains B<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                      complement of A<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                      the closure of A<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                       empty set<p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman" size=3>(</FONT><v:shape><FONT face="Times New Roman"><FONT size=3> <v:imagedata></v:imagedata></FONT></FONT></v:shape><FONT face="Times New Roman" size=3>) i=1,2,…,r  j=1,2,…,s   r-by-s</FONT><FONT size=3>(<FONT face="Times New Roman">r</FONT>×<FONT face="Times New Roman">s</FONT>)<FONT face="Times New Roman">matrix<p></p></FONT></FONT></P>
<P ><FONT size=3>│</FONT><v:shape><FONT face="Times New Roman"><FONT size=3> <v:imagedata></v:imagedata></FONT></FONT></v:shape><FONT size=3>│<FONT face="Times New Roman">I,j=1,2,…,n </FONT>    <FONT face="Times New Roman">determinant of order n<p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman" size=3>det(</FONT><v:shape><FONT face="Times New Roman"><FONT size=3> <v:imagedata></v:imagedata></FONT></FONT></v:shape><FONT face="Times New Roman" size=3>)                  the determinant of the matrix (</FONT><v:shape><FONT face="Times New Roman"><FONT size=3> <v:imagedata></v:imagedata></FONT></FONT></v:shape><FONT face="Times New Roman"><FONT size=3>) <p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                      vector F<p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman" size=3>x=(</FONT><v:shape><FONT face="Times New Roman"><FONT size=3> <v:imagedata></v:imagedata></FONT></FONT></v:shape><FONT face="Times New Roman" size=3>,</FONT><v:shape><FONT face="Times New Roman"><FONT size=3> <v:imagedata></v:imagedata></FONT></FONT></v:shape><FONT face="Times New Roman" size=3>,…,</FONT><v:shape><FONT face="Times New Roman"><FONT size=3> <v:imagedata></v:imagedata></FONT></FONT></v:shape><FONT face="Times New Roman" size=3>)          x is an n-tuple of </FONT><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3> <p></p></FONT></FONT></P>
<P ><FONT size=3>‖‖          <FONT face="Times New Roman">the norm of …<p></p></FONT></FONT></P>
<P ><FONT size=3>‖<FONT face="Times New Roman">                      parallel to<p></p></FONT></FONT></P>
<P ><FONT size=3>┴<FONT face="Times New Roman">                      perpendicular to<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                      the exponential function of x<p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman"><FONT size=3>lin x                     the logarithmic function of x<p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman"><FONT size=3>sie                      sine<p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman"><FONT size=3>cos                      cosine<p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman"><FONT size=3>tan                      tangent<p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman"><FONT size=3>sinh                     hyperbolic sine<p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman"><FONT size=3>cosh                     hyperbolic cosine<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                     the inverse of f<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                 f is the composite or the composition of u and v<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                   the limit of …as n approaches </FONT></FONT><FONT size=3>∞</FONT><FONT face="Times New Roman" size=3>(as x approaches</FONT><v:shape><FONT face="Times New Roman"><FONT size=3> <v:imagedata></v:imagedata></FONT></FONT></v:shape><FONT face="Times New Roman"><FONT size=3>)<p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman" size=3>x</FONT><v:shape><FONT face="Times New Roman"><FONT size=3> <v:imagedata></v:imagedata></FONT></FONT></v:shape><FONT face="Times New Roman"><FONT size=3>a                    x approaches a<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman" size=3>,</FONT><v:shape><FONT face="Times New Roman"><FONT size=3> <v:imagedata></v:imagedata></FONT></FONT></v:shape><FONT face="Times New Roman"><FONT size=3>                  the differential coefficient of y; the 1st derivative of y<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman" size=3>,</FONT><v:shape><FONT face="Times New Roman"><FONT size=3> <v:imagedata></v:imagedata></FONT></FONT></v:shape><FONT face="Times New Roman"><FONT size=3>               the nth derivative of y<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                the partial derivative of f with respect to x<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                the partial derivative of f with respect to y<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                 the indefinite integral of f<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                the definite integral of f between a and b (from a to b)<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                   the increment of x<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                   differential x<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                 summation of …the sum of the terms indicated<p></p></FONT></FONT></P>
<P ><FONT size=3>∏          <FONT face="Times New Roman">the product of the terms indicated<p></p></FONT></FONT></P>
<P ><FONT face="Times New Roman"><FONT size=3>=&gt;                    implies<p></p></FONT></FONT></P>
<P ><v:shape><v:imagedata><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><FONT face="Times New Roman"><FONT size=3>                 is equivalent to<p></p></FONT></FONT></P>
<P ><FONT size=3>(<FONT face="Times New Roman"> </FONT>)<FONT face="Times New Roman">                 round brackets; parantheses<p></p></FONT></FONT></P>
<P ><FONT size=3><FONT face="Times New Roman">[  ]                   square brackets<p></p></FONT></FONT></P>
<P ><FONT size=3><FONT face="Times New Roman">{  }                  braces<p></p></FONT></FONT></P>
<P ><FONT size=3><FONT face="Times New Roman"> <p></p></FONT></FONT></P>
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